Efficient Two-Electron Ansatz for Benchmarking Quantum Chemistry on a Quantum Computer

Abstract

Quantum chemistry provides key applications for near-term quantum computing, but these are greatly complicated by the presence of noise. In this work we present an efficient ansatz for the computation of two-electron atoms and molecules within a hybrid quantum-classical algorithm. The ansatz exploits the fundamental structure of the two-electron system, and treating the nonlocal and local degrees of freedom on the quantum and classical computers, respectively. Here the nonlocal degrees of freedom scale linearly with respect to basis-set size, giving a linear ansatz with only $\mathcal{O}(1)$ circuit preparations required for reduced state tomography. We implement this benchmark with error mitigation on two publicly available quantum computers, calculating accurate dissociation curves for 4- and 6- qubit calculations of ${\mathrm{H}}_{\text{2}}^{}$ and ${\mathrm{H}}_{\text{3}}^{+}$.

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• Hybrid quantum-classical neural network for calculating ground state energies of molecules
• Error statistics and scalability of quantum error mitigation formulas
• The Basics of Quantum Computing for Chemists
• Lowering Tomography Costs in Quantum Simulation with a Symmetry Projected Operator Basis
• Error-Mitigated Quantum Simulation of Interacting Fermions with Trapped Ions
• Precision ground-state energy calculation for the water molecule on a superconducting quantum processor
• Quantum Simulation of Quantum Phase Transitions Using the Convex Geometry of Reduced Density Matrices
• Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function
• Refining ensemble $N$-representability of one-body density matrices from partial information